A maths course · nothing assumed
Ground Up
Start at what the equals sign actually claims. Finish at gradient descent. Every idea arrives with something you can grab and move.
No memorising
Rules you memorise fall off. Every rule here is derived in front of you from something you can see, so you can rebuild it whenever it slips.
Break things on purpose
Each idea comes with an instrument. Drag it to absurd values. What refuses to break is what is actually true.
It lands on code
Every section ends by cashing out in something you already write — floating point, bit shifts, hash collisions, cost functions.
The route
Modules 0 to 2 rebuild the ground. From module 3 on, every lesson ends in something you would actually ship.
Module 0
The Ground Floor
Everything else stands on these three lessons.
You stop guessing and start seeing.
- 0.1The Ground FloorWhat the equals sign actually claims, fractions as frozen division, the one rule behind every exponent, variables as boxes, and rearranging without fear.40 min
- 0.2Below ZeroA minus sign is a direction, not a disaster. The three jobs one symbol does, and why two negatives multiply to a positive — shown, not asserted.30 min
- 0.3Shapes of GrowthSlope as rate, straight lines as promises, and the difference between speeding up and slowing down — read off shapes rather than numbers.30 min
Module 1
Counting in Other Languages
Ten fingers was an accident of biology. Machines have two.
Binary stops being trivia and starts being obvious.
- 1.1Base Ten Was a ChoiceWhat a digit position really means, why zero had to be invented, and how to count in any base at all.30 min
- 1.2Binary and HexReading a byte on sight, why hex is sixteen and not ten, and the fact that every colour you have written is three bytes.30 min
- 1.3Negative Numbers in a Box of BitsTwo's complement as one seat turning negative, why flip-and-add-one builds a negative rather than drawing one, and overflow as a dial with no edges.30 min
- 1.4Why 0.1 + 0.2 Is Not 0.3Binary fractions, why one tenth is binary's one third, what a double actually stores, and the autopsy showing the addition was never the bug.35 min
Module 2
True and False
The maths your if-statements are made of.
You can simplify a condition on paper and trust it.
- 2.1Boolean AlgebraTrue and false as values rather than questions, AND and OR as arithmetic, and short-circuit as a promise about what will not run.30 min
- 2.2De Morgan's TradePushing a NOT through a bracket flips the operator — and why almost every bug here is an English bug rather than a logic one.25 min
- 2.3Sets Are Your Data StructuresUnion, intersection and difference as boolean operators applied to membership — plus why every diff you have read is three set operations.30 min
Module 3
Wrapping Around
Clock arithmetic, which turns out to run the internet.
Hashing, checksums and cryptography stop being magic.
Module 4
How Many Ways
Counting things too big to count one at a time.
You can size a search space before you write the loop.
Module 5
How Fast
The maths of whether your code survives real data.
Big-O becomes something you can feel, not recite.
Module 6
How Likely
Reasoning about things that have not happened yet.
Retries, load, caching and A/B tests stop being vibes.
Module 7
Arrows and Grids
Linear algebra, taught as movement rather than notation.
Graphics, embeddings and ML stop looking like hieroglyphs.
Module 8
Angles and Waves
Trigonometry, starting from a point going round a circle.
Rotation, orbits and oscillation stop needing memorised formulas.
- 8.1The Unit CircleSine and cosine as the coordinates of a point walking round a circle — not ratios in a triangle. Where atan2 comes from and why it exists.35 min
- 8.2Turning ThingsRotating a point about the origin, why the rotation matrix looks the way it does, and radians as the unit that stops the formulas needing constants.35 min
- 8.3WavesSine as oscillation rather than geometry — amplitude, frequency, phase. Audio, easing curves and anything that repeats.35 min
Module 9
Change
Calculus, arrived at honestly.
You build gradient descent yourself and know why it works.
- 9.1Zooming In Until It Looks StraightLimits, without the epsilon ceremony. The idea first.35 min
- 9.2The Derivative Is a Steepness MeterDrag a point along a curve and read its slope as you go.40 min
- 9.3Rolling DownhillGradient descent, built step by step, on a cost surface you can tilt.45 min
- 9.4Adding Up Infinitely Many SliversIntegration as accumulation, and where it shows up in code.40 min